Sure, let's walk through the problem step-by-step.
1. Understand the Problem:
- We need to calculate the cost of an item in 1939, given its cost in 1930 and the Consumer Price Index (CPI) for both years.
2. Given Data:
- CPI for 1930: 16.7
- CPI for 1939: 13.9
- Cost in 1930: [tex]$100
3. Formula to Use:
To find the equivalent cost in another year when CPI values are given, the formula is:
\[
\text{Cost in 1939} = \left( \frac{\text{Cost in 1930}}{\text{CPI in 1930}} \right) \times \text{CPI in 1939}
\]
4. Substitute the Given Values into the Formula:
\[
\text{Cost in 1939} = \left( \frac{100}{16.7} \right) \times 13.9
\]
5. Calculate Step-by-Step:
- First, divide the cost in 1930 by the CPI in 1930:
\[
\frac{100}{16.7} \approx 5.988
\]
- Next, multiply the result by the CPI in 1939:
\[
5.988 \times 13.9 \approx 83.2232
\]
6. Round to Two Decimal Places:
- The final step is to round 83.2232 to two decimal places, which is 83.23.
Therefore, the cost of the item in 1939 would be $[/tex]83.23.
